Why were there twelve labours of Heracles, not ten?

The Labours of Heracles

The Delphic oracle tells Heracles to serve Eurystheus at Tiryns for twelve years and complete ten labours; Eurystheus later refuses to count two of the ten, so two more are added and the tally reaches twelve. Apollodorus lists the twelve in one order, the Temple of Zeus at Olympia carves them in another, and the two accounts do not even agree on whether the last of them, the fetching of Cerberus, belongs in the sequence at all.

In short

The Pythia at Delphi names Alcides 'Hercules' for the first time and sends him to serve Eurystheus at Tiryns for twelve years, performing ten labours, not twelve (Apollodorus, Library 2.4.12).
Eurystheus refuses to count the Lernaean hydra, because Iolaus helps land the blow, and the Augean stables, because Heracles had agreed a price with Augeas for the work (Apollodorus, Library 2.5.2, 2.5.5).
The two refusals, not two extra deeds, are why the count reaches twelve: 'Eurystheus ordered Hercules, as an eleventh labour, to fetch golden apples from the Hesperides, for he did not acknowledge the labour of the cattle of Augeas nor that of the hydra' (Library 2.5.11).
The Temple of Zeus at Olympia, built 470–456 BC, carries all twelve on its metopes, six over the pronaos and six over the opisthodomos, the earliest surviving set to fix the labours in stone.
Pausanias's own description of those metopes ends on the cleansing of the Augean stables and never names Cerberus at all (Description of Greece 5.10.9).
Pausanias records two unreconciled traditions about the first Olympic games at Olympia: an earlier Cretan Dactyl also named Heracles is said to have held and named them, and, generations later, Heracles son of Amphitryon, the labours' Heracles, held them again after conquering Elis (5.7.6, 5.7.9, 5.8.3).

Ten labours, set at Delphi

Hera drives Heracles mad, and in his madness he kills his own children. Purified and in exile, he asks the Delphic oracle where he should live. The Pythia calls him Hercules for the first time, in place of Alcides, and tells him to settle at Tiryns and serve Eurystheus for twelve years, performing ten labours Eurystheus is to set him; when the tasks are done, she says, he will be immortal (Apollodorus, Library 2.4.12).

Apollodorus’s sequence runs from the Nemean lion, Hydra, hind and boar through the stables, birds, bull, mares, belt and cattle, then ends with the Hesperides’ apples and Cerberus. The oracle asked for ten. The list reaches twelve only because Eurystheus rejects two tasks along the way.

The two Eurystheus would not count

The hydra is disqualified for one reason: Heracles does not beat it alone. His nephew Iolaus helps him keep the severed heads from growing back, so Eurystheus rules that Iolaus’s part has made the labour invalid (Library 2.5.2).

The Augean stables are disqualified for a different reason. Before starting the work, Heracles strikes a bargain with King Augeas, a tenth of the herd for clearing the dung in a single day, without telling him Eurystheus has ordered it. Eurystheus voids this one too, “alleging that it had been performed for hire”: a job done for pay, not a labour performed as commanded (Library 2.5.5).

Two refusals, out of ten, leave eight standing. After eight years and a month, Eurystheus orders the apples as an eleventh labour because he has refused both the stables and the Hydra (Library 2.5.11). Cerberus becomes the twelfth. These last tasks replace the two struck from the original ten.

A different order at Olympia

Apollodorus’s Library was compiled long after the labours already had a temple to their name. The Temple of Zeus at Olympia, built 470–456 BC, carries all twelve in relief on its metopes, and the Museum of Classical Archaeology at Cambridge, which holds cast reproductions of them, credits the scheme with “contributing greatly” to the labours being “quantified as a canonical twelve” in the first place.

Pausanias describes the set two centuries after he saw it. One side carried the boar, Diomedes, Geryon’s cattle, Atlas and the stables; the other carried the Amazon’s belt, deer, bull, birds, Hydra and lion. His sentence names eleven labours. Cerberus is absent.

Long before Apollodorus set down his list, Euripides had already made the opposite choice about where the cycle ends. His chorus in the Heracles works through the lion, the deer, the apples, the belt, the hydra and the cattle of Geryon, then turns to the last of them: Heracles “has now sailed” to the house of Hades, “the goal of his labors” (Heracles 425–427). For Euripides as for Apollodorus, the descent for the Hound of Hades is where the count ends. At Olympia, on Pausanias’s account of it, that is exactly the labour left out.

Pausanias records another disagreement about Olympia. Elean antiquaries credit the earliest games to a different Heracles, one of five Cretan Dactyls guarding the infant Zeus. Later in the same book, Heracles son of Amphitryon holds them after conquering Elis. Both founders remain in his text.

What stands on the ground

The German Archaeological Institute excavated the Temple of Zeus in 1875–76, and the metopes came out of the ground in pieces. Most are now in the Archaeological Museum of Olympia; the Atlas panel is in the Louvre as Louvre 716.

On the Argolid plain, Tiryns is the citadel the oracle names. It is where the Pythia sends Heracles to serve Eurystheus, and where, on Apollodorus’s account, a frightened Eurystheus first refuses to let him past the gates and has him display the proof of each labour outside the walls instead (Library 2.4.12, 2.5.1). The German Archaeological Institute has excavated Tiryns on and off since Heinrich Schliemann began there in 1876, and the Cyclopean walls that gave the masonry style its name still stand over the citadel.

Where to stand

Nafplio

Peloponnese

In Apollodorus, the Pythia sends Heracles to Tiryns to serve Eurystheus for twelve years, and it is there, after the first labour, that a frightened Eurystheus bars him from the city and has him show the proof of each labour at the gates instead. The killing of the Nemean lion and the Lernaean hydra, the first two labours on every list, both belong to the same stretch of Argolid plain around the citadel.
Nafplio
Olympia

Peloponnese

The Temple of Zeus at Olympia carries all twelve labours on its metopes, six above the pronaos and six above the opisthodomos, though Pausanias's own description of them ends on the cleansing of the Augean stables and never mentions Cerberus. Pausanias also records two unreconciled traditions about the first games at Olympia, one crediting an earlier Cretan Dactyl also named Heracles, the other crediting Heracles son of Amphitryon, who held them again after conquering Elis.
Olympia